名校
1 . 已知函数
.
(1)若函数
有唯一零点,求实数
的取值范围;
(2)若对任意实数
,对任意
,恒有
成立,求正实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69aa6dcfa396b68b5141814d4789858.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38aa6c2f221e36a8d80f8c182ffe2b93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb10d63dee91e86640cffd2f926dc17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d758175ade18283cb7d7e0e7b05478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa9c6d1c4999faeb1de657d0b87a6fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-12-26更新
|
1378次组卷
|
6卷引用:吉林省长春市东北师范大学附属中学2022-2023学年高一上学期阶段验收考试数学试题
吉林省长春市东北师范大学附属中学2022-2023学年高一上学期阶段验收考试数学试题陕西省西北工业大学附属中学2022-2023学年高一上学期1月期末模拟数学试题湖北省华中师范大学第一附属中学2022-2023学年高一下学期2月月考数学试题陕西省西安市长安区第一中学2023-2024学年高一上学期期末考试数学试题河南省周口市太康县第一高级中学2023-2024学年高一上学期1月月考数学试题(已下线)第六章 导数与不等式恒成立问题 专题九 双变量不等式恒成立问题 微点1 值域法破解双变量不等式恒成立问题
名校
2 . 函数
.
(1)若
的最小值为0,求a的值;
(2)对于集合
,若任意的
,总存在
,使得
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0d56de6d5c9d0f15c89835d4f2b419.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)对于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54813454c88186b073ab2d2539c2f269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a0ac8b620b5eca9daa7276712935ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea818a4506f4b158f85e721b60c86c.png)
您最近一年使用:0次
2022-12-12更新
|
1239次组卷
|
2卷引用:广东省清远市四校2022-2023学年高一上学期联合学业质量检测数学试题
名校
解题方法
3 . 已知函数
为定义在
上的偶函数,当
时,
.
(1)当
时,作出函数
的图象,并指出其单调区间;
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/fa4956f0-4879-42f6-a0d5-9075c39ab19b.png?resizew=231)
(2)若函数
有两个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43fc02238be01c1448778e8b4af0e663.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/fa4956f0-4879-42f6-a0d5-9075c39ab19b.png?resizew=231)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d667165b4280fde15e00ebe585edec8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
4 . 集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbcace4afbfc0f54dcc48bb0027421d.png)
,其中
为正整数.对
中的任意元素
和
,定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4792cb732db55a4e316194b8dce162.png)
(1)当
时,求
和
的值.
(2)当
时,
的子集
满足:对
中任意元素
和
不能被
整除,且当
时,
能被
整除.求集合
中元素个数的最大值.
(3)给定
的子集
满足:对
中任意元素
和
,当
不等于
时,
.求集合
中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbcace4afbfc0f54dcc48bb0027421d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6560671eeefa4dbeffee99e5b6cbb340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862fa87bae8adc1812c8a388540ffeab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e44f3369474465aead73a72de28e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4792cb732db55a4e316194b8dce162.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf566d23dea97f8fe28cebd1ed1f6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b55e4da087f72dbae9e2b267fe8d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f96befc97fd01907c8ee93b77654e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5946132021868ed3dd54f1c8ff8f13b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f96befc97fd01907c8ee93b77654e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)给定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c56eb0dd21760e45b92fbe0e3098786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdff4c5bc8d38fdf36c1887e4c72f373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
5 . 已知函数
,
,其中
,
.
(1)若
,求函数
在
上的值域;
(2)若函数
恰好有三个零点
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a72eeeef8313692965bf5ddae91407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a56807f295dc1a2c56a2cb2fb70dc42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf2f46bc120e5b6f8317b02370bffbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ba2c12fa14a6f63de6b628b495393a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f65ae14389e6904956bd88df4450e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
6 . 函数
,方程
有三个互不相等的实数根,从小到大依次为
.
(1)当
时,求
的值;
(2)求符合题意的
的取值范围;
(3)若对于任意符合题意的
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f95842e86d20c4cfb0db08675cbc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c543b45884d75765b16c78bcd0e149.png)
(2)求符合题意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若对于任意符合题意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e18c65d75a24393e4d814da3b8f9f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2022-12-01更新
|
909次组卷
|
2卷引用:黑龙江省哈尔滨师范大学附属中学2022-2023学年高一上学期期中考试数学试题
名校
解题方法
7 . 函数
,方程
有三个互不相等的实数根,从小到大依次为
,
,
.
(1)当
时,求
的值;
(2)若对于任意的正实数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b4a647a94dca12e07814d9d9f7a79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c543b45884d75765b16c78bcd0e149.png)
(2)若对于任意的正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e18c65d75a24393e4d814da3b8f9f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
,
.
(1)若不等式
对任意
,
恒成立,求实数
的取值范围;
(2)对于
,求函数
在
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19235af93513ae52117810409db6b8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12724c29358aa4ab11a2269072d6bc4f.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aad29a5dea066766fa0ba45bacb5829.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e135a02718e057f697cff737853c564f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbfd726516bbd901771a5482cce35301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
您最近一年使用:0次
2022-11-29更新
|
1308次组卷
|
3卷引用:江苏省淮安市淮阴中学2022-2023学年高一上学期期中数学试题
江苏省淮安市淮阴中学2022-2023学年高一上学期期中数学试题浙江省嘉兴市第一中学2023-2024学年高一上学期10月月考数学试题(已下线)第二篇 函数与导数专题5 切比雪夫、帕德逼近 微点4 切比雪夫逼近与帕德逼近综合训练
名校
解题方法
9 . 设定义在
上的函数
满足:①对
,
,都有
;②
时,
;③不存在
,使得
.
(1)求证:
为奇函数;
(2)求证:
在
上单调递增;
(3)设函数
,
,不等式
对
恒成立,试求
的值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cccdff49c3efe6e7a7dbbf69db9319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f09285f931bc3754410b6dffa53e4ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e532d7fd74b192af0eb6ab598971a8b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b017ec7de129a26a325c52db6a3abfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321b6c58f9bcbbcf99ba037e3bd4497a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8265a52147b71939bf1f37eba52c609b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6552c3a42c2629ef9533f0fc651736.png)
您最近一年使用:0次
2022-11-18更新
|
2042次组卷
|
4卷引用:湖北省鄂东南省级示范高中教育教学改革联盟学校2022-2023学年高一上学期期中联考数学试题
名校
解题方法
10 . 设A是非空实数集,且
.若对于任意的
,都有
,则称集合A具有性质
;若对于任意的
,都有
,则称集合A具有性质
.
(1)写出一个恰含有两个元素且具有性质
的集合A;
(2)若非空实数集A具有性质
,求证:集合A具有性质
;
(3)设全集
,是否存在具有性质
的非空实数集A,使得集合
具有性质
?若存在,写出这样的一个集合A;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72552b86b4558a36aac78c7148d6a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae4f0ccdfc1206d809e581449d0452e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4970b63e04ae03e833bdb95bd52e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
(1)写出一个恰含有两个元素且具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(2)若非空实数集A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
(3)设全集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a8afa6857b5eaf945d14a6e4d7e5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c093cbde3d3472d1f7f2b0dff2bc4881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
您最近一年使用:0次
2022-11-17更新
|
621次组卷
|
7卷引用:上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题
上海市南洋模范中学2022-2023学年高一上学期开学考试数学试题(已下线)专题01集合与逻辑(15个考点)(1)(已下线)专题1.8 集合与常用逻辑用语全章综合测试卷(提高篇)-举一反三系列(已下线)重难点01集合与常用逻辑用语(9种解题模型与方法)(1)(已下线)专题03集合的运算1-【倍速学习法】(沪教版2020必修第一册)北京市东城区2021-2022学年高二下学期期末统一检测数学试题北京市顺义牛栏山第一中学2022-2023学年高二下学期6月月考数学试题